President Obama signed the historic health care bill into law today, but Republicans are still fighting back with promises of lawsuits and heated rhetoric, including a shot from one GOP governor who blasted what he called Obama's "nanny nation approach" to government.

The individual mandate is an "unprecedented overreach by the federal government forcing individual citizens to buy a good or a service for no other reason then they happen to be alive or a person," Republican governor of Minnesota Tim Pawlenty said today on "Good Morning America."

Pawlenty said he sent a letter to Minnesota's Democratic attorney general arguing against the constitutionality of the mandate.

"They've taken it to this big, federalized, bureaucratic, government-run, kind of nanny nation approach," Pawlenty said. "I don't think defending the Constitution and individual's rights under the Constitution, and the relationship between states and the federal government under the Constitution is a frivolous matter."

David Axelrod Defends Health Care

Twelve state attorneys general, all of whom are Republican, have already filed suits to block the health care bill on the grounds that its requirement that everyone have health insurance is unconstitutional. Four state legislatures have already passed laws blocking the bill. On Wednesday, Virginia's GOP Gov. Bob McDonnell will sign the bill into the state's law, making it illegal for the federal government to require Americans to purchase health insurance.

Senior White House adviser David Axelrod dismissed the lawsuits, saying the Obama administration is very confident the health care bill "will withstand those legal challenges.

Republican Backlash Over Health Care

"First of all, every single major piece of legislation that's ever been passed in this country has engendered lawsuits. That's the nature of our system, and we expected that," Axelrod said on "GMA." "We're not concerned about these lawsuits."

Watch live coverage of President Obama signing the health care bill at 11:15 a.m. ET on ABC News network or streamed live on ABCNews.com.

Under the health care bill, by 2014 most Americans would be required to have health insurance or pay a fine, with the exception of low-income Americans. Employers would also be required to provide coverage to their workers, or pay a fine of $2,000 per worker. Companies with fewer than 50 employees, however, are exempt from this rule.

Like many of his GOP counterparts, Pawlenty assailed the partisan nature of the health care bill. The legislation did not garner one single Republican "yes" vote in the House, which passed the bill Sunday night.

"There were 10 or 15 really good reforms that both sides could've agreed on," Pawlenty said. "They [Democrats] were more interested in achieving that ideological or political goal rather than working with Republicans to get something done."

Republicans are regrouping and gearing up to use the health care bill against their Democratic opponents in November's midterm elections. Ads blasting Democrats who were going to vote "yes" for the health care bill filled the airwaves well before the bill was even passed.